On the form and location of the Psychometric Bisection Function for time

Abstract

The Psychometric Bisection Function for time relates the discriminability of intermediate duration stimuli to a short and long training duration. Bisection Functions for animals ( R. M. Church & M. Z. Deluty, Journal of Experimental Psychology: Animal Behavior Processes, 1977 , 3, 216–228) confirm Weber's Law and also show indifference between short and long reports at the geometric mean of the training durations. Two discrimination processes are studied which, in combination with different constructions of the subjective time scale, result in Bisection Functions which differ in form and location. The two discrimination processes use a likelihood ratio rule or a similarity rule to compare intermediate durations to the training durations. These rules in combination with two different constructions of the subjective time scale result in four models which conform to Weber's Law. For one of the scales subjective time is a power function of real time with the scalar property on variance (Scalar Timing). For the other, subjective time is a logarithmic function of real time with constant variance (Log Timing). Both Log and Scalar Timing assume normality on the subjective scale. Only three of these models also entail the geometric mean at the indifference point. The exception is Scalar Timing with the likelihood ratio discrimination rule. This model entails indifference at approximately the harmonic mean of the training stimuli. Variants of the remaining three models differ theoretically but alternatives are difficult to discriminate empirically. A contrast is provided by a Poisson Timing subjective scale in which variance increases directly with the mean. This scale results in indifference at the geometric mean for both discrimination rules but violates Weber's Law in both cases.